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Short-distance Schwinger-mechanism and chiral symmetry

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      Abstract

      In this paper, we study Schwinger pair production of charged massless particles in constant electric fields of finite-extent. Exploiting a map from the Dirac and Klein-Gordon equation to the harmonic oscillator, we find exact pair production rates for massless fermions and scalars. Pair production rates depend only on the ratio between the capacitor plate separation, \(\ell\), and the length-scale of the force-field, \(\ell_F\). Chirality ensures that fermion production smoothly vanishes with \(\ell/\ell_F\). Scalar pair production though diverges exponentially quickly in this limit. The same limit of the smooth tanh-potential does not diverge; divergences seem tied to singularities in current and charge densities.

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          This is a colloquium-style introduction to two electronic processes in a carbon monolayer (graphene), each having an analogue in relativistic quantum mechanics. Both processes couple electron-like and hole-like states, through the action of either a superconducting pair potential or an electrostatic potential. The first process, Andreev reflection, is the electron-to-hole conversion at the interface with a superconductor. The second process, Klein tunneling, is the tunneling through a p-n junction. Existing and proposed experiments on Josephson junctions and bipolar junctions in graphene are discussed from a unified perspective. CONTENTS: I. INTRODUCTION II. BASIC PHYSICS OF GRAPHENE (Dirac equation; Time reversal symmetry; Boundary conditions; Pseudo-diffusive dynamics) III. ANDREEV REFLECTION (Electron-hole conversion; Retro-reflection vs. specular reflection; Dirac-Bogoliubov-de Gennes equation; Josephson junctions; Further reading) IV. KLEIN TUNNELING (Absence of backscattering; Bipolar junctions; Magnetic field effects; Further reading) V. ANALOGIES (Mapping between NS and p-n junction; Retro-reflection vs. negative refraction; Valley-isospin dependent quantum Hall effect; Pseudo-superconductivity)
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            Author and article information

            Journal
            09 November 2017
            1711.03504

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            11 pages, 6 figures
            hep-th cond-mat.str-el hep-ph

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